Data Studio: Changing Default Data Source

Yes, you can. But remember when you connect a new data source you may need to rebuild charts if DS doesn't know which data sources are the same. However, as you say, with you connecting to GA you will only need to do this once to get a report which automatically updates.

You could remove the data source at report level, add a new one, then work through all your charts - or add the new data source to your charts one at a time at chart level.